Question

Determine the equation of the graph and select the correct answer below.

1. y = (x + 3)2 − 2
2. y = (x − 3)2 − 2
3. y = (x + 3)2 + 2
4. y = (x − 3)2 + 2

Answer 1

3)
`y=(x+3)^2+2`

Explanation:

The vertex for a quadratic equation is given by:

`y=a(x-h)^2+k`

Where
`a` ≠0 and
`(h,k)` is the vertex of the the curve.

From the graph we see that the vertex is
`(-3,2)`

Thus the equation of the graph can be written as:

`y=a(x-(-3))^2+2`

`y=a(x+3)^2+2`

Given y-intercept on the graph
`(0,11)`

Plugging in point of y-intercept in the equation we got in order to find
`a`

`11=a(0+3)^2+2`

`11=a(3)^2+2`

`11=9a+2`

Subtracting both sides by 2.

`11-2=9a+2-2`

`9=9a`

Dividing both sides by 9.

`(9)/(9)=(9a)/(9)`

∴
`a=1`

So the equation of graph is

`y=(1)(x+3)^2+2`

`y=(x+3)^2+2`